On Hardy kernels as reproducing kernels
Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 428-442
Voir la notice de l'article provenant de la source Cambridge
Hardy kernels are a useful tool to define integral operators on Hilbertian spaces like $L^2(\mathbb R^+)$ or $H^2(\mathbb C^+)$. These kernels entail an algebraic $L^1$-structure which is used in this work to study the range spaces of those operators as reproducing kernel Hilbert spaces. We obtain their reproducing kernels, which in the $L^2(\mathbb R^+)$ case turn out to be Hardy kernels as well. In the $H^2(\mathbb C^+)$ scenario, the reproducing kernels are given by holomorphic extensions of Hardy kernels. Other results presented here are theorems of Paley–Wiener type, and a connection with one-sided Hilbert transforms.
Mots-clés :
Reproducing kernel Hilbert spaces, Hardy kernels, Laplace transform
Oliva-Maza, Jesús. On Hardy kernels as reproducing kernels. Canadian mathematical bulletin, Tome 66 (2023) no. 2, pp. 428-442. doi: 10.4153/S0008439522000406
@article{10_4153_S0008439522000406,
author = {Oliva-Maza, Jes\'us},
title = {On {Hardy} kernels as reproducing kernels},
journal = {Canadian mathematical bulletin},
pages = {428--442},
year = {2023},
volume = {66},
number = {2},
doi = {10.4153/S0008439522000406},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000406/}
}
Cité par Sources :